This vignette demonstrates how to back-calculate lengths at previous ages from radial measurements made on calcified structures of fish. This vignette assumes that you have an understanding of
combineData() to combine R data files
created from digitizeRadii() and join fish-specific
information as described in the Collecting Radii Data vignette.Packages used in this vignette are loaded below.
library(RFishBC) # for bcFuns()
library(FSA) # for validn(), sumTable()
library(dplyr) # for %>%, inner_join(), arrange(), group_by, summarize()Finally, some of the data manipulations used in this vignette, which may not be familiar to all readers, are described in detail in Ogle (2016).
The radial measurements from multiple fish should be combined into
one data.frame using combineData(). In addition, the
length-at-capture for each fish should be appended to that data.frame. A
method to combine radial measurements from multiple fish and append a
length-at-capture variable was demonstrated in the Output Data File section of the
Collecting Radii Data vignette.
Several of the back-calculation methods require estimating parameters from the relationship between fish length and structure radius or structure radius and fish length (as described in Short Introduction to Back-calculation vignette). These methods cannot be demonstrated well with a small number of fish (as in the Collecting Radii Data vignette). Thus, data from a large number of Smallmouth Bass (Micropterus dolomieu) collected from West Bearskin Lake (MN) in 1990 will be used in this vignette.
A data.frame of the Smallmouth Bass data as it would appear from
combineData() is obtained as follows.1
data(SMBassWB2,package="RFishBC")
head(SMBassWB2)
#> id reading agecap radcap rad1 rad2 rad3 rad4 rad5 rad6 rad7 rad8 rad9
#> 1 482 DHO 1 1.51076 1.51076 NA NA NA NA NA NA NA NA
#> 2 768 DHO 1 1.57989 1.57989 NA NA NA NA NA NA NA NA
#> 3 428 DHO 1 1.48721 1.48721 NA NA NA NA NA NA NA NA
#> 4 478 DHO 2 2.73596 1.60554 2.73596 NA NA NA NA NA NA NA
#> 5 379 DHO 2 3.05503 1.59628 3.05503 NA NA NA NA NA NA NA
#> 6 477 DHO 2 2.44914 1.32061 2.44914 NA NA NA NA NA NA NAA data.frame of fish-specific information, most importantly the length-at-capture, is obtained as follows.2
data(SMBassWB1,package="RFishBC")
head(SMBassWB1)
#> id species lake gear yearcap lencap
#> 1 5 SMB WB E 1988 71
#> 2 3 SMB WB E 1988 64
#> 3 2 SMB WB E 1988 57
#> 4 4 SMB WB E 1988 68
#> 5 6 SMB WB E 1988 72
#> 6 7 SMB WB E 1988 80These data can be joined by the common id variable as
shown in the Output Data File
section of the Collecting Radii Data vignette. The data were also
arranged by id to facilitate comparisons throughout this
vignette.3
SMBassWB <- inner_join(SMBassWB1,SMBassWB2,by="id") %>%
arrange(id)
head(SMBassWB,n=3)
#> id species lake gear yearcap lencap reading agecap radcap rad1 rad2
#> 1 374 SMB WB E 1990 243 DHO 7 7.57375 1.01672 2.39296
#> 2 375 SMB WB E 1990 293 DHO 7 9.74397 1.76579 3.26580
#> 3 376 SMB WB E 1990 214 DHO 7 5.34522 1.02621 1.93058
#> rad3 rad4 rad5 rad6 rad7 rad8 rad9
#> 1 3.47635 4.37718 5.18976 6.09176 7.57375 NA NA
#> 2 4.35377 5.41608 7.14118 8.79697 9.74397 NA NA
#> 3 2.58000 3.24923 4.05444 4.73920 5.34522 NA NA
tail(SMBassWB,n=3)
#> id species lake gear yearcap lencap reading agecap radcap rad1 rad2
#> 179 767 SMB WB E 1990 99 DHO 2 2.34205 1.44159 2.34205
#> 180 768 SMB WB E 1990 75 DHO 1 1.57989 1.57989 NA
#> 181 998 SMB WB E 1990 298 DHO 7 8.54805 1.37828 2.70647
#> rad3 rad4 rad5 rad6 rad7 rad8 rad9
#> 179 NA NA NA NA NA NA NA
#> 180 NA NA NA NA NA NA NA
#> 181 3.60701 4.48222 5.17646 6.6224 8.54805 NA NANote that the variables in this data frame are defined as follows:4
A data.frame of back-calculated lengths (\(L_{i}\)) can be constructed from a
data.frame that contains at least the length-at-capture (\(L_{cap}\)), structure radius-at-capture
(\(R_{cap}\)), and the structure radius
at each annulus (\(R_{i}\)) with
backCalc().
The first argument to this function is a data.frame with the \(L_{cap}\), \(R_{cap}\), and \(R_{i}\) data in either “long” or “wide” format. A long-format data.frame MUST have the following variable names:
id: Unique fish identification variable.agecap: The fish’s age at capture.ann: The annulus number.rad: The structure radius (at an annulus).radcap: The total structure radius at the time of
capture.A wide-format data.frame MUST have the following variable names:
id: Unique fish identification variable.agecap: The fish’s age at capture.radcap: The total structure radius at the time of
capture.radX: Multiple variables that contain the structure
radius to the Xth annulus.These data.frames will be in these required formats if the data
originated from the combineData() function.5 Other variables may
exist in the data.frame, but these variables must exist with the names
and contents shown here.
The data.frame MUST also have a variable that
contains the fish’s length-at-capture. The name for this variable
MUST be given (without quotes) in the second or
lencap= argument.
The format for the input data.frame MUST be given in
inFormat=. The two choices for this argument are
"long" and "wide".
Finally, one of the many back-calculation models discussed in
Vigliola and Meekan (2009) must be selected for use with the
BCM= argument. The back-calculation model can be chosen by
“name” or number, both of which can be seen in the documentation for
bcFuns(). For example, the popular Fraser-Lee model can
be selected with BCM="FRALE" or BCM=2.
Some of the models require parameters estimated from models fit to
the relationship between fish length and structure radius or structure
radius and fish length. These models will be fit “behind-the-scenes” in
backCalc(). However, some models also require parameters
estimated without the observed data, which must then be provided by the
user. For example, the Fraser-Lee model uses a length correction factor
that may be the estimated length when the structure first forms or a
standard published value for a species (Carlander 1980). If the user
wants to provide one of these values, then it is given in the
a= argument.6 Other parameters for other models may be
given in other arguments to backCalc() (see the documentation for
backCalc()).
The results of backCalc() can be returned in either
“long” or “wide” format as identified with outFormat=
(which defaults to be the same as inFormat=). The number of
digits for the back-calculated lengths may be controlled with
digits=.
For example, back-calculated lengths were constructed from the
wide-format data in SMBassWB, which has length-at-capture
data in the lencap variable, using the Fraser-Lee model
(with the “a” parameter estimated from the data) with the code below.
The lengths were rounded to whole numbers (i.e., digits=0)
and the results were returned in wide-format (the same as the input
format).
SMBassWB_FL <- backCalc(SMBassWB,lencap,BCM="FRALE",inFormat="wide",digits=0)
#> ✔ Using the Fraser-Lee model with a=41.6516606795388.
head(SMBassWB_FL,n=3)
#> # A tibble: 3 × 17
#> id species lake gear yearcap lencap reading agecap len1 len2 len3
#> <dbl> <fct> <fct> <fct> <int> <int> <chr> <int> <dbl> <dbl> <dbl>
#> 1 374 SMB WB E 1990 243 DHO 7 69 105 134
#> 2 375 SMB WB E 1990 293 DHO 7 87 126 154
#> 3 376 SMB WB E 1990 214 DHO 7 75 104 125
#> # ℹ 6 more variables: len4 <dbl>, len5 <dbl>, len6 <dbl>, len7 <dbl>,
#> # len8 <dbl>, len9 <dbl>
tail(SMBassWB_FL,n=3)
#> # A tibble: 3 × 17
#> id species lake gear yearcap lencap reading agecap len1 len2 len3
#> <dbl> <fct> <fct> <fct> <int> <int> <chr> <int> <dbl> <dbl> <dbl>
#> 1 767 SMB WB E 1990 99 DHO 2 77 99 NA
#> 2 768 SMB WB E 1990 75 DHO 1 75 NA NA
#> 3 998 SMB WB E 1990 298 DHO 7 83 123 150
#> # ℹ 6 more variables: len4 <dbl>, len5 <dbl>, len6 <dbl>, len7 <dbl>,
#> # len8 <dbl>, len9 <dbl>The example below uses the same data and same back-calculation model, but with the results returned in long-format which is more conducive to statistical summarization and modeling.
SMBassWB_FL2 <- backCalc(SMBassWB,lencap,BCM="FRALE",
inFormat="wide",outFormat="long",digits=0)
#> ✔ Using the Fraser-Lee model with a=41.6516606795388.
head(SMBassWB_FL2,n=6)
#> # A tibble: 6 × 10
#> id species lake gear yearcap lencap reading agecap ann bclen
#> <dbl> <fct> <fct> <fct> <int> <int> <chr> <int> <dbl> <dbl>
#> 1 374 SMB WB E 1990 243 DHO 7 1 69
#> 2 374 SMB WB E 1990 243 DHO 7 2 105
#> 3 374 SMB WB E 1990 243 DHO 7 3 134
#> 4 374 SMB WB E 1990 243 DHO 7 4 158
#> 5 374 SMB WB E 1990 243 DHO 7 5 180
#> 6 374 SMB WB E 1990 243 DHO 7 6 204
tail(SMBassWB_FL2,n=6)
#> # A tibble: 6 × 10
#> id species lake gear yearcap lencap reading agecap ann bclen
#> <dbl> <fct> <fct> <fct> <int> <int> <chr> <int> <dbl> <dbl>
#> 1 998 SMB WB E 1990 298 DHO 7 2 123
#> 2 998 SMB WB E 1990 298 DHO 7 3 150
#> 3 998 SMB WB E 1990 298 DHO 7 4 176
#> 4 998 SMB WB E 1990 298 DHO 7 5 197
#> 5 998 SMB WB E 1990 298 DHO 7 6 240
#> 6 998 SMB WB E 1990 298 DHO 7 7 298
For example, the mean back-calculated length-at-age may be computed
with group_by() and summarize() as shown below
for the long-format Fraser-Lee results.
tmp <- SMBassWB_FL2 %>%
group_by(ann) %>%
summarize(n=validn(bclen),
mn=round(mean(bclen),0),
sd=round(sd(bclen),1)) %>%
as.data.frame()
tmp
#> ann n mn sd
#> 1 1 181 79 6.5
#> 2 2 178 114 10.5
#> 3 3 155 147 13.9
#> 4 4 71 173 15.3
#> 5 5 64 201 17.5
#> 6 6 64 235 23.3
#> 7 7 50 269 25.3
#> 8 8 2 283 26.9
#> 9 9 2 314 20.5Additionally, the mean length at each back-calculated age computed
separately for each age-at-capture is found with
sumTable(), where the left side of the formula is the
quantitative variable to be summarized and the right side has grouping
variables presented in row*column format.
sumTable(bclen~agecap*ann,data=SMBassWB_FL2,digits=0)
#> 1 2 3 4 5 6 7 8 9
#> 1 74 NA NA NA NA NA NA NA NA
#> 2 80 113 NA NA NA NA NA NA NA
#> 3 77 113 149 NA NA NA NA NA NA
#> 4 71 122 161 194 NA NA NA NA NA
#> 6 80 108 136 169 199 230 NA NA NA
#> 7 82 118 145 171 202 237 269 NA NA
#> 9 72 100 135 166 198 236 256 283 314
Carlander, K.D. 1982. Standard intercepts for calculating lengths from scale measurements for some centrarchid and percid fishes. Transactions of the American Fisheries Society 111:332–336. Abstract
Ogle, D.H. 2016. Introductory Fisheries Analyses with R. CRC Press/Chapman & Hall. Webpage
Vigliola, L., and M.G. Meekan. 2009. The back-calculation of fish growth from otoliths. Pages 174-211 in Green, B., B. Mapstone, G. Carlos, and G. Begg, editors. Tropical fish otoliths: information for assessment, management and ecology, volume 11. Springer, Dordrecht, Netherlands. Full Text
Both of these data.frames are available in the
RFishBC package. However, these types of data could be the
result of using comineData() and inner_join()
or from loading a relevant CSV file as demonstrated in Output Data File section of the
Collecting Radii Data vignette.↩︎
Note that this file contains information from fish captured in years other than 1990.↩︎
Arranging the data by fish id is not required for the work below. It is simply used here for demonstration purposes.↩︎
The species, lake,
gear, yearcap, and reading
variables are not needed in this vignette, but could be needed in
further statistical analyses.↩︎
If your data originated from somewhere else, then you may need to rename your variables to meet these conventions.↩︎
If a is not provided by the user for the
Fraser-Lee model, then it will be estimated from the intercepts of the
linear regression of fish length on structure radius.↩︎